Report of the fit

Fit summary

Description: PV19 version x, parameters for NNLL
Minimiser: ceres
Random seed: 1234
Maximum values allowed for q_T / Q: 0.2
Percentile cut: 5
Parameterisation: PV19x
Initial parameters fluctuations: True
Explicit formula:

f_{\rm NP}(x,\zeta, b_T)= \Biggl( \frac{1-\lambda}{1 + g_1(x) b_T^2/4} + \lambda \exp \left(-g_{1B}(x) b_T^2 / 4 \right)\Biggr) \exp\left[- g_2 \log\left(\frac{\zeta}{Q_0^2}\right) b_T^2/4 - g_{2B} \log\left(\frac{\zeta}{Q_0^2}\right) b_T^4/4 \right]g_1(x) = \frac{N_1}{x\sigma} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha}\right)}{2 \sigma^2} \right]g_{1B}(x) = \frac{N_{1B}}{x\sigma_B} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha_B}\right)}{2 \sigma_B^2} \right]Q_0^2 = 1\;{\rm GeV}^2 t_0 prescription: True

g_2 N_1 \alpha \sigma \lambda N_{1B} \alpha_B \sigma_B g_{2B}
-0.05651150850119966 1.6027888644000163 0.7249039013242403 0.9073457205932122 0.3543394928378163 0.020375939002791388 0.09386203899849682 0.0274857746762149 0.019920085284356754

Theory summary

Collinear PDF set: MMHT2014nlo68cl member 0
Collinear FF set: DSS14_NLO_PiSum member 0
b^* prescription: bstarmin
Perturbative order: NNLL
Reference value of the fine-structure constant: \alpha(Q = 91.1876\;{\rm GeV}) = 0.00776578395589 (running True)

Global statistical estimators

N_{rep} = 123
\chi_{0}^2 = 1.6686
\chi_{mean}^2 = 1.6187
\langle\chi^2\rangle \pm \sigma_{\chi^2} = 1.699 \pm 0.0179
\langle E \rangle \pm \sigma_{E} = 2.7067 \pm 0.1822

Parameters

Parameter Central replica Average over replicas Fixed
g_2 -0.057632624 -0.06067214 \pm 0.00991237 False
N_1 2.9759481 3.9825571 \pm 2.90529141 False
\alpha 1.1506021 1.44479698 \pm 0.82949205 False
\sigma 1.0075239 1.04188758 \pm 0.12926533 False
\lambda 0.41068867 0.38967438 \pm 0.05760985 False
N_{1B} 0.020634549 0.01698134 \pm 0.02448685 False
\alpha_B 0.093901444 0.08480947 \pm 0.01835043 False
\sigma_B 0.027372726 0.07070338 \pm 0.22613747 False
g_{2B} 0.022667287 0.0221229 \pm 0.00389806 False
Fitted parameter correlation matrix

Fit properties

Global \chi^2 distribution
Global error function distribution
g_2 distribution
N_1 distribution
\alpha distribution
\sigma distribution
\lambda distribution
N_{1B} distribution
\alpha_B distribution
\sigma_B distribution
g_{2B} distribution

Table of \chi^2’s

Central-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.6238 0.1214 0.7452
E605_Q_8_9 8 1.3045 0.0691 1.3736
E605_Q_10.5_11.5 10 0.3757 0.1109 0.4866
E605_Q_11.5_13.5 12 0.8441 0.5623 1.4064
E605_Q_13.5_18 13 1.5147 0.8465 2.3612
E288_200_Q_4_5 4 0.7664 0.7988 1.5652
E288_200_Q_5_6 5 2.1307 0.4234 2.5541
E288_200_Q_6_7 6 0.7444 0.2812 1.0257
E288_200_Q_7_8 7 0.8839 0.0264 0.9103
E288_200_Q_8_9 8 0.6539 0.0276 0.6815
E288_300_Q_4_5 4 0.6072 0.1654 0.7725
E288_300_Q_5_6 5 1.1438 0.0536 1.1973
E288_300_Q_6_7 6 0.7982 0.0225 0.8208
E288_300_Q_7_8 7 0.2511 0.0364 0.2876
E288_300_Q_8_9 8 0.4295 0.0385 0.468
E288_300_Q_11_12 9 0.3634 0.2529 0.6163
E288_400_Q_5_6 5 0.5715 0.0304 0.6019
E288_400_Q_6_7 6 0.2342 0.0352 0.2694
E288_400_Q_7_8 7 0.0678 0.0442 0.112
E288_400_Q_8_9 8 0.4449 0.0392 0.4841
E288_400_Q_11_12 11 0.4828 0.0234 0.5062
E288_400_Q_12_13 12 0.5065 0.0338 0.5403
E288_400_Q_13_14 12 0.3174 0.0814 0.3988
STAR_510 7 1.2387 0.01 1.2486
CDF_RunI 25 0.7072 0.144 0.8512
CDF_RunII 26 1.3213 0.01 1.3313
D0_RunI 12 0.7239 0.0022 0.7262
D0_RunII 5 0.7471 0.2832 1.0303
D0_RunIImu 3 0.0917 0.0626 0.1542
LHCb_7TeV 7 1.8719 0.84 2.7119
LHCb_8TeV 7 1.575 1.4168 2.9918
LHCb_13TeV 7 1.3457 0.2828 1.6285
CMS_7TeV 4 2.9143 0 2.9143
CMS_8TeV 4 1.5396 0.1872 1.7268
ATLAS_7TeV_y_0_1 6 7.3245 1.0659 8.3904
ATLAS_7TeV_y_1_2 6 5.305 0.4723 5.7773
ATLAS_7TeV_y_2_2.4 6 1.9714 0.0117 1.9831
ATLAS_8TeV_y_0_0.4 6 5.2343 1.0322 6.2665
ATLAS_8TeV_y_0.4_0.8 6 7.0149 1.5624 8.5772
ATLAS_8TeV_y_0.8_1.2 6 4.3759 0.6204 4.9962
ATLAS_8TeV_y_1.2_1.6 6 2.9863 0.386 3.3723
ATLAS_8TeV_y_1.6_2 6 2.8329 0.2559 3.0888
ATLAS_8TeV_y_2_2.4 6 2.2342 0.2927 2.5268
ATLAS_8TeV_Q_46_66 4 0.8297 0.0468 0.8764
ATLAS_8TeV_Q_116_150 8 1.2064 0.0081 1.2144
Total 353 - - 1.6686
Mean-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 1.0413 0.1653 1.2067
E605_Q_8_9 8 1.9883 0.0692 2.0574
E605_Q_10.5_11.5 10 0.289 0.1021 0.3912
E605_Q_11.5_13.5 12 0.4054 0.3274 0.7328
E605_Q_13.5_18 13 0.4925 0.4774 0.9699
E288_200_Q_4_5 4 0.3056 0.3168 0.6225
E288_200_Q_5_6 5 0.9947 0.2239 1.2186
E288_200_Q_6_7 6 0.3204 0.1594 0.4798
E288_200_Q_7_8 7 0.5654 0.031 0.5963
E288_200_Q_8_9 8 0.7568 0.0124 0.7692
E288_300_Q_4_5 4 0.3959 0.0655 0.4614
E288_300_Q_5_6 5 0.7728 0.0311 0.8039
E288_300_Q_6_7 6 0.4961 0.0182 0.5143
E288_300_Q_7_8 7 0.1204 0.0309 0.1513
E288_300_Q_8_9 8 0.3481 0.0395 0.3876
E288_300_Q_11_12 9 1.1611 0.1952 1.3563
E288_400_Q_5_6 5 0.5332 0.0536 0.5868
E288_400_Q_6_7 6 0.1591 0.0472 0.2063
E288_400_Q_7_8 7 0.0282 0.0521 0.0803
E288_400_Q_8_9 8 0.571 0.038 0.6091
E288_400_Q_11_12 11 0.6297 0.0147 0.6445
E288_400_Q_12_13 12 0.705 0.0203 0.7253
E288_400_Q_13_14 12 0.5264 0.0758 0.6022
STAR_510 7 1.0982 0.033 1.1312
CDF_RunI 25 0.5492 0.1396 0.6888
CDF_RunII 26 1.277 0.0054 1.2824
D0_RunI 12 0.7523 0.0008 0.7531
D0_RunII 5 0.6181 0.2753 0.8934
D0_RunIImu 3 0.1504 0.0802 0.2306
LHCb_7TeV 7 1.7073 0.8373 2.5446
LHCb_8TeV 7 1.6073 1.3343 2.9416
LHCb_13TeV 7 1.2351 0.2661 1.5012
CMS_7TeV 4 2.9437 0 2.9437
CMS_8TeV 4 1.6294 0.2037 1.8331
ATLAS_7TeV_y_0_1 6 7.8261 1.0375 8.8636
ATLAS_7TeV_y_1_2 6 5.4844 0.4931 5.9775
ATLAS_7TeV_y_2_2.4 6 2.2383 0.0132 2.2515
ATLAS_8TeV_y_0_0.4 6 5.6345 1.0816 6.7161
ATLAS_8TeV_y_0.4_0.8 6 7.1082 1.6795 8.7877
ATLAS_8TeV_y_0.8_1.2 6 4.5226 0.6608 5.1834
ATLAS_8TeV_y_1.2_1.6 6 3.0431 0.4013 3.4444
ATLAS_8TeV_y_1.6_2 6 2.8589 0.2841 3.143
ATLAS_8TeV_y_2_2.4 6 3.0846 0.3833 3.4678
ATLAS_8TeV_Q_46_66 4 0.832 0.0766 0.9087
ATLAS_8TeV_Q_116_150 8 1.2569 0.0044 1.2614
Total 353 - - 1.6187
Average-over-replicas \chi^2’s:
Experiment Number of points \chi^2
E605_Q_7_8 7 0.7432 \pm 0.1616
E605_Q_8_9 8 1.4255 \pm 0.2666
E605_Q_10.5_11.5 10 0.5176 \pm 0.0553
E605_Q_11.5_13.5 12 1.4606 \pm 0.1141
E605_Q_13.5_18 13 2.3576 \pm 0.1744
E288_200_Q_4_5 4 1.6882 \pm 0.2984
E288_200_Q_5_6 5 2.5667 \pm 0.2263
E288_200_Q_6_7 6 1.0203 \pm 0.1495
E288_200_Q_7_8 7 0.881 \pm 0.1447
E288_200_Q_8_9 8 0.6676 \pm 0.0623
E288_300_Q_4_5 4 0.8535 \pm 0.1861
E288_300_Q_5_6 5 1.2042 \pm 0.1686
E288_300_Q_6_7 6 0.7994 \pm 0.1787
E288_300_Q_7_8 7 0.2826 \pm 0.0889
E288_300_Q_8_9 8 0.4933 \pm 0.0435
E288_300_Q_11_12 9 0.6226 \pm 0.074
E288_400_Q_5_6 5 0.5998 \pm 0.1633
E288_400_Q_6_7 6 0.2682 \pm 0.1374
E288_400_Q_7_8 7 0.1264 \pm 0.0959
E288_400_Q_8_9 8 0.5005 \pm 0.0706
E288_400_Q_11_12 11 0.5285 \pm 0.0732
E288_400_Q_12_13 12 0.5632 \pm 0.0512
E288_400_Q_13_14 12 0.3997 \pm 0.0756
STAR_510 7 1.2353 \pm 0.0904
CDF_RunI 25 0.8573 \pm 0.0399
CDF_RunII 26 1.4921 \pm 0.217
D0_RunI 12 0.7562 \pm 0.0507
D0_RunII 5 1.2175 \pm 0.3092
D0_RunIImu 3 0.2007 \pm 0.1525
LHCb_7TeV 7 2.722 \pm 0.0744
LHCb_8TeV 7 3.0174 \pm 0.1745
LHCb_13TeV 7 1.6371 \pm 0.0402
CMS_7TeV 4 2.921 \pm 0.0166
CMS_8TeV 4 1.7485 \pm 0.0684
ATLAS_7TeV_y_0_1 6 8.4585 \pm 0.2608
ATLAS_7TeV_y_1_2 6 5.8815 \pm 0.1855
ATLAS_7TeV_y_2_2.4 6 1.9866 \pm 0.1213
ATLAS_8TeV_y_0_0.4 6 6.2521 \pm 0.2219
ATLAS_8TeV_y_0.4_0.8 6 8.6274 \pm 0.1297
ATLAS_8TeV_y_0.8_1.2 6 5.0667 \pm 0.15
ATLAS_8TeV_y_1.2_1.6 6 3.4761 \pm 0.1573
ATLAS_8TeV_y_1.6_2 6 3.2569 \pm 0.2928
ATLAS_8TeV_y_2_2.4 6 2.2757 \pm 0.4488
ATLAS_8TeV_Q_46_66 4 0.8699 \pm 0.0244
ATLAS_8TeV_Q_116_150 8 1.2264 \pm 0.0262
Total 353 1.699 \pm 0.0179

TMDs in k_T space

TMD PDF of the d at Q = 2 GeV and x = 0.001
TMD PDF of the d at Q = 2 GeV and x = 0.01
TMD PDF of the d at Q = 2 GeV and x = 0.1
TMD PDF of the d at Q = 2 GeV and x = 0.5
TMD PDF of the d at Q = 2 GeV and x = 0.9

Data-theory comparison

E605_Q_7_8 data-theory comparison
E605_Q_8_9 data-theory comparison
E605_Q_10.5_11.5 data-theory comparison
E605_Q_11.5_13.5 data-theory comparison
E605_Q_13.5_18 data-theory comparison
E288_200_Q_4_5 data-theory comparison
E288_200_Q_5_6 data-theory comparison
E288_200_Q_6_7 data-theory comparison
E288_200_Q_7_8 data-theory comparison
E288_200_Q_8_9 data-theory comparison
E288_300_Q_4_5 data-theory comparison
E288_300_Q_5_6 data-theory comparison
E288_300_Q_6_7 data-theory comparison
E288_300_Q_7_8 data-theory comparison
E288_300_Q_8_9 data-theory comparison
E288_300_Q_11_12 data-theory comparison
E288_400_Q_5_6 data-theory comparison
E288_400_Q_6_7 data-theory comparison
E288_400_Q_7_8 data-theory comparison
E288_400_Q_8_9 data-theory comparison
E288_400_Q_11_12 data-theory comparison
E288_400_Q_12_13 data-theory comparison
E288_400_Q_13_14 data-theory comparison
STAR_510 data-theory comparison
CDF_RunI data-theory comparison
CDF_RunII data-theory comparison
D0_RunI data-theory comparison
D0_RunII data-theory comparison
D0_RunIImu data-theory comparison
LHCb_7TeV data-theory comparison
LHCb_8TeV data-theory comparison
LHCb_13TeV data-theory comparison
CMS_7TeV data-theory comparison
CMS_8TeV data-theory comparison
ATLAS_7TeV_y_0_1 data-theory comparison
ATLAS_7TeV_y_1_2 data-theory comparison
ATLAS_7TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_y_0_0.4 data-theory comparison
ATLAS_8TeV_y_0.4_0.8 data-theory comparison
ATLAS_8TeV_y_0.8_1.2 data-theory comparison
ATLAS_8TeV_y_1.2_1.6 data-theory comparison
ATLAS_8TeV_y_1.6_2 data-theory comparison
ATLAS_8TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_Q_46_66 data-theory comparison
ATLAS_8TeV_Q_116_150 data-theory comparison